Proxy Vector Autoregressions in a Data-rich Environment

Bayesian Vector Autoregressions

This article provides an introduction to the burgeoning academic literature on Bayesian Vector Autoregressions, benchmark models for applied macroeconomic research. We first explain Bayes’ theorem and the derivation of the closed-form solution for the posterior distribution of the parameters of the model given data. We further consider parameter shrinkage, a distinguishing feature of the prior ...

Vector Autoregressions and Cointegration*

Prior Selection for Vector Autoregressions∗

Vector autoregressions (VARs) are flexible time series models that can capture complex dynamic interrelationships among macroeconomic variables. However, their dense parameterization leads to unstable inference and inaccurate out-ofsample forecasts, particularly for models with many variables. A potential solution to this problem is to use informative priors, in order to shrink the richly param...

Priors about Observables in Vector Autoregressions

Standard practice in Bayesian VARs is to formulate priors on the autoregressive parameters, but economists and policy makers actually have priors about the behavior of observable variables. We show how this kind of prior can be used in a VAR under strict probability theory principles. We state the inverse problem to be solved and we propose a numerical algorithm that works well in practical sit...

Data-based priors for vector autoregressions with drifting coefficients

This paper proposes full-Bayes priors for time-varying parameter vector autoregressions (TVP-VARs) which are more robust and objective than existing choices proposed in the literature. We formulate the priors in a way that they allow for straightforward posterior computation, they require minimal input by the user, and they result in shrinkage posterior representations, thus, making them approp...